ADDITIONAL MATHEMATICS 0606/11 - Past Papers

Cambridge IGCSE™

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DC (PQ/FC) 187997/3© UCLES 2020 [Turn over

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ADDITIONAL MATHEMATICS 0606/11

Paper 1 October/November 2020

2 hours

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● You should use a calculator where appropriate. ● You must show all necessary working clearly; no marks will be given for unsupported answers from a

calculator. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in

degrees, unless a different level of accuracy is specified in the question.

INFORMATION ● The total mark for this paper is 80. ● The number of marks for each question or part question is shown in brackets [ ].

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Mathematical Formulae

1. ALGEBRA

Quadratic Equation

For the equation ax bx c 02 + + = ,

x ab b ac

242!

=- -

Binomial Theorem

( )a b a a b a b a bn n n

r b1 2n n n n n r r n1 2 2 f f+ = + + + ++ +- - -e e eo o o

where n is a positive integer and ( ) ! !

!nr n r r

n=-

e o

Arithmetic series ( )u a n d1n = + -

( ) { ( ) }S n a l n a n d21

21 2 1n = + = + -

Geometric series u arnn 1= -

( )

( )S ra r

r11

1n

n!=

--

( )S ra r1 11=-3

2. TRIGONOMETRY

Identities

sin cosA A 12 2+ =sec tanA A12 2= +eccos cotA A12 2= +

Formulae for ∆ABC

sin sin sinAa

Bb

Cc

= =

cosa b c bc A22 2 2= + -

sinbc A21T =

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1

- 2 - 1 0 4

24

y

x

The diagram shows the graph of ( )y xp= , where ( )xp is a cubic function. Find the two possible expressions for ( )xp . [3]

2 (a) Write down the amplitude of cos x1 4 3+ b l. [1]

(b) Write down the period of cos x1 4 3+ b l. [1]

(c) On the axes below, sketch the graph of cosy x1 4 3= + b l for x180 180° ° °G G- .

- 60 60 120 180x

y

0- 120- 180

1

2

3

4

5

6

[3]

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3 (a) Write p

q p r

qr3 1 3

2 31

-``jj

in the form p q ra b c , where a, b and c are constants. [3]

(b) Solve x x6 5 1 032

31

- + = . [3]

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4 It is given that sintany x

x3= .

(a) Find the exact value of xy

dd

when x 3r

= . [4]

(b) Hence find the approximate change in y as x increases from 3r to h3

r+ , where h is small. [1]

(c) Given that x is increasing at the rate of 3 units per second, find the corresponding rate of change in y when x 3

r= , giving your answer in its simplest surd form. [2]

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5 (a) (i) Find how many different 4-digit numbers can be formed using the digits 1, 3, 4, 6, 7 and 9. Each digit may be used once only in any 4-digit number. [1]

(ii) How many of these 4-digit numbers are even and greater than 6000? [3]

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(b) A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if

(i) there are no restrictions, [1]

(ii) the committee contains at least one doctor, [2]

(iii) the committee contains all the nurses. [1]

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6 A particle P is initially at the point with position vector 3010e o and moves with a constant speed of

10ms 1- in the same direction as 43-e o.

(a) Find the position vector of P after t s. [3]

As P starts moving, a particle Q starts to move such that its position vector after t s is given by

t8090

512

-+e eo o.

(b) Write down the speed of Q. [1]

(c) Find the exact distance between P and Q when t 10= , giving your answer in its simplest surd form. [3]

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7 It is given that ( ) ( )lnx x5 2 3f = + for x 232- .

(a) Write down the range of f. [1]

(b) Find f 1- and state its domain. [3]

(c) On the axes below, sketch the graph of ( )y xf= and the graph of ( )y xf 1= - . Label each curve and state the intercepts on the coordinate axes.

O

y

x

[5]

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8 (a) (i) Show that ( ) ( )cosec sin sin

sec1

12

2

i i ii

+ -= . [4]

(ii) Hence solve ( ) ( )cosec sin sin1 432i i i+ - = for ° °180 180G Gi- . [4]

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(b) Solve sin cos3 32 3 3

2r rz z+ = +e eo o for 0 3

2G G

rz radians, giving your answers in terms of r.

[4]

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9 (a) Given that lnx x x12 31 3d

a

1-

+=e oy , where a 02 , find the exact value of a, giving your answer

in simplest surd form. [6]

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(b) Find the exact value of sin cosx x x2 3 1 2 d0

r3 r

+ - +e b l oy . [5]

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10 (a) An arithmetic progression has a second term of 8 and a fourth term of 18. Find the least number of terms for which the sum of this progression is greater than 1560. [6]

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(b) A geometric progression has a sum to infinity of 72. The sum of the first 3 terms of this progression

is 8333 .

(i) Find the value of the common ratio. [5]

(ii) Hence find the value of the first term. [1]

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To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series.

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ADDITIONAL MATHEMATICS 0606/11 - Past Papers